Zeitgeist 2008  --  the spirit, trends, thoughts and feelings characteristic of our time. Blog Subscribe . Mandelbrots Iterating functions Mandelbrots, named after Benoit Mandelbrot are defined by a process of iterating functions. Above is an image of the Mandelbrot set in a complex parameter plane. The displayed portion includes the rectangle -0.500000 < x < 0.500000, -0.500000 < y < 1.500000 displayed as an image 500 pixels wide by 30 pixels high. The Mandelbrot formula Given a complex function, f(z), and a complex number, z(0), consider the sequence z(0), f(z(0)), f(f(z(0))), . . . known as the orbit of z(0) under f(z). The magnitude of a complex number a + bi is the real number that is the distance from the point representing the complex number and the origin. This is the square root of (a*a + b*b). f(n)(z(0)) is defined to be the nth term in the orbit of z(0) under f(z), where f(0)(z(0)) = z(0). If there exists M > 0 such that the absolute value of f(n)(z(0)) is <= M for all n, then the orbit of z(0) under f(z) is said to be bounded. Otherwise, the orbit of z(0) under f(z) is said to escape to infinity. Creating your own Mandelbrots The Mandelbrots may be created by coloring the pixels at each point on the function based on the number of iterations needed for the orbit to escape to infinity. It is possible to generate an infinite variety of Mandelbrots either by programing your computer to run the Mandelbrot iteration formula or by using one of these programs: the David Joyce Mandelbrot Applet the Eclectasy Fractal-Explorer To use the progams, input your real and imaginary coordinates and selecting a number of iterations and colors.   Zeitgeist  |  Forums  |  Jokes  |  Games  |  Poker  |  Digital Consciousness  |  Contact   Bodog software, developed in-house by our poker-crazed designers, allows for fast game action and slick graphics. Use this link for a 10% Cash Signup Bonus. Poker World owned by Olympic Sports, one of the most respected names in online gaming, offers a wide range of guaranteed tournaments and promotions and a lucrative rewards program. Use this link for a 20% topless deposit bonus. True Poker -- Realistic audio and 3-D image technology. Use this link for a 30% first deposit bonus. Ultimate Bet where virtually everyone plays poker. Use this link for a 40% first deposit bonus on deposits of $25 or more up to $200.